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I am currently studying Nodal Analysis using Engineering Circuit Analysis (8th Ed., pp. 80-81) by Hayt, Kemmerly, and Durbin.

In Figure 4.1(d), the author applies Kirchhoff’s Current Law (KCL) to Node 1 to derive Equation 1. The author's equation is:

$$\frac{v_1}{2} + \frac{v_1 - v_2}{5} = 3.1$$

I am having trouble understanding the derivation. In my view, the reference potential \$v_{\text{Ref.}}\$ is missing from the first term. I believe the author's equation is only valid if we assume \$v_{\text{Ref.}} = 0 \text{V}\$.

If I apply KCL to Node 1 without assuming the reference is zero, I would write:

$$\frac{v_1 - v_{\text{Ref.}}}{2} + \frac{v_1 - v_2}{5} = 3.1$$

My question: Can someone please clarify what my mistake is, or explain the author's logic behind omitting \$v_{\text{Ref.}}\$ from the equation?

See the screenshot from the textbook below highlighted in red: enter image description here

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    \$\begingroup\$ Since Vref would substract from every voltage, it simply cancels out. Give it a try. \$\endgroup\$ Commented Feb 24 at 17:09
  • \$\begingroup\$ Hello @ScottSeidman, Thanks for your comment. Since yesterday, I’ve been trying to figure out how to cancel out \$v_{\text{Ref.}}\$, but I haven’t been able to make it work. Could you give me a hint? I applied KCL at both nodes including \$v_{\text{Ref.}}\$, but it doesn’t cancel out. I end up with two equations (two KCL's) and three unknowns: \$v_{1}\$, \$v_{2}\$, \$v_{\text{Ref.}}\$. \$\endgroup\$ Commented Feb 25 at 6:34

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In the caption of Figure 4.1 (d) authors have clearly mentioned that a ground symbol can be used to depict the reference node.

enter image description here

GND or Reference is always considered as 0V while implementing nodal analaysis.

You can assume the Ref. node as 0V. There's nothing wrong with this nomenclature.

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  • \$\begingroup\$ thank a ton anit. now its clear. however why the author does not clearly draw the ground symbol in the circuit? \$\endgroup\$ Commented Feb 24 at 13:51
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    \$\begingroup\$ @MarcoMoldenhauer, May be they were lazy? But not really. Try reading the last 3 paragraphs on page 80 of your book again. Pay special attention to the following sentence in the book: "If there is a ground node, it is usually most convenient to select it as the reference node, although many people seem to prefer selecting the bottom node of a circuit as the reference, especially if no explicit ground is noted." Hopefully it will clear your doubt. Thanks. \$\endgroup\$ Commented Feb 24 at 14:04
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\$V_{ref}\$ is ground and it is supposed to be at 0V. \$V_1 - V_{ref} = V_1 \$.

The nodal equations are correct.

Writing nodal equations,

$$\frac{V_1 - V_{ref}}{2} + \frac{V_1 - V_2}{5} = 3.1 \tag1$$

$$\frac{V_2 - V_{ref}}{1} + \frac{V_2 - V_1}{5} = 1.4 \tag2$$

Solve these two linear equations for \$V_1\$ and \$V_2\$

If you want \$V_{ref}\$ to be non zero,that would yield two different equations from the book.

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